For the reaction: $A_{(g)} + B_{(s)} \rightleftharpoons 2C_{(g)} + D_{(g)}$,given $\Delta U = 5.0 \ kcal$ and $\Delta S = 50 \ cal \ K^{-1}$ at $400 \ K$. Calculate $\Delta G$ for the reaction. (in $kcal$)

The difference between $\Delta H$ and $\Delta U$ $(\Delta H - \Delta U),$ when the combustion of one mole of heptane $(l)$ is carried out at a temperature $T$ is equal to (in $,RT$)

Calculate the enthalpy change on freezing of $1.0 \ mol$ of water at $10.0^{\circ} C$ to ice at $-10.0^{\circ} C$. Given: $\Delta_{fus} H = 6.03 \ kJ \ mol^{-1}$ at $0^{\circ} C$,$C_p [H_2 O_{(l)}] = 75.3 \ J \ mol^{-1} \ K^{-1}$,$C_p [H_2 O_{(s)}] = 36.8 \ J \ mol^{-1} \ K^{-1}$.

Calculate the standard internal energy change for $OF_{2(g)} + H_2O_{(g)} \longrightarrow 2 HF_{(g)} + O_{2(g)}$ at $300 \ K$,if $\Delta_{f} H^{\circ}$ of $OF_{2(g)}$,$H_2O_{(g)}$,and $HF_{(g)}$ are $20$,$-250$,and $-270 \ kJ \ mol^{-1}$ respectively. $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$ (in $kJ$)

Arrange the following isothermal processes in order of the magnitude of the work $(w)$ involved between states $1$ and $2$.
$A$. Expansion in single stage $(w_A)$
$B$. Expansion in multi stages $(w_B)$
$C$. Compression in single stage $(w_C)$
$D$. Compression in multi stages $(w_D)$

When $1 \ g$ of $NH_4NO_3$ is decomposed in a bomb calorimeter,the temperature of the calorimeter increases by $6.12 \ K$. If the heat capacity of the system is $1.23 \ kJ/K$,the molar enthalpy of decomposition of $NH_4NO_3$ is ........ $kJ/mol$.